(I rarely run it off the battery, because recharging it will eventually wear it out, and I really don't want to have to find a way to spare the money to replace it. Yes, my finances are THAT bad.)
You're probably thinking of the old "memory effect" of nickel cadmium batteries. Modern lithium ion batteries don't have that effect. Keeping the battery in the laptop constantly will not cause trickle charging to reduce the capacity of the battery.
There *is* a small advantage to removing the battery, but it is not the one you're thinking of. The biggest stress on modern lithium batteries is heat: the hotter they are, the faster they lose their charging lifetime, and ironically this effect is stronger when the battery is at full charge than when it is at low charge. However, unless your laptop runs extremely hot, the effect is probably not worth the headache of constantly removing and replacing the battery.
Most modern laptops do allow you to hot plug the battery, but I don't recommend doing that often. You're just as likely to wear out the battery contacts through constant swapping than the battery capacity itself. Regardless, as chuckv3 states, nothing you do will keep the battery perfect forever, and if the only reason you need the battery is to keep the laptop powered for the few minutes it takes to move it to another room then I'd just keep the battery in. Even at 10% capacity that's more than enough time to do that. A laptop battery is likely to contain enough charge for a room move for seven to ten years (in three to five you probably don't want it powering your laptop at a Starbucks without AC power) and you can get third party replacements for $50-$75. 75 bucks every ten years is almost certainly less than what you're paying in electrical costs to power the laptop.
A word on deep discharge. Don't do it. I know chuckv3 recommended doing that every six month. I strongly advise against it. Some people recommend doing a battery meter calibration cycle on the laptop so you know the battery fuel gauge is accurate, and if that's important to you go ahead. But given how you're using it, I don't think the fuel gauge is all that important. Lithium ion batteries do not like deep discharge. Every deep discharge you do is probably hurting the battery as much as couple months of shallow discharge usage. The NiCads used to like that. Lithium ion does not.